A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting by 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

let the unit digit and the ten's digit of the number be x and y respectively.

therefore the number = 10y + x.

sum of digits = x+y

difference of the digits = y-x [if x < y]

multiply eq(1) by 3 and subtracting eq(2):

substitute x =3 in eq(1):

thus the unit digit of the number is 3 and ten's digit is 8.

thus number is 83.

hope this helps you.

cheers!!

**
**